Alexander Sistko

activity

20162025

F_{1}

-Representations, and Euler Characteristics of Quiver Grassmannians

4 citations · 6 across the 9 of their papers we have counts for

collaborators

11 papers

math.CT2025

Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves

Jaiung Jun, Alex Sistko, Cameron Wright

We study the category $F$ - $Mat_{∙}$ of matroids over an idyll $F$ . We show that $F$ - $Mat_{∙}$ is a proto-exact category, a non-additive generalization of…

math.RT2025

On Semisimple Proto-Abelian Categories Associated to Inverse Monoids

Alexander Sistko

Let $G$ be a finite abelian group written multiplicatively, with $G^= G ⊔ {0}$ the pointed abelian group formed by adjoining an absorbing element $0$ . There is an assoc…

math.RT2023★ 1 cited

On the Combinatorics of $F_{1}$ -Representations of Pseudotree Quivers

Jaiung Jun, Jaehoon Kim, Alex Sistko

We investigate quiver representations over $F_{1}$ . Coefficient quivers are combinatorial gadgets equivalent to $F_{1}$ -representations of quivers. We focus on the ca…

math.RT2022

Pointed Hopf Algebras of Discrete Corepresentation Type

Miodrag Iovanov, Emre Sen, Alexander Sistko +1

We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$ , we explicitly determine th…

math.RT2021★ 4 cited

Coefficient Quivers, $F_{1}$ -Representations, and Euler Characteristics of Quiver Grassmannians

Jaiung Jun, Alex Sistko

A quiver representation assigns a vector space to each vertex, and a linear map to each arrow. When one considers the category $Vect (F_{1})$ of vector spaces ``over…

math.RT2020

On quiver representations over $F_{1}$

Jaiung Jun, Alex Sistko

We study the category $Rep (Q, F_{1})$ of representations of a quiver $Q$ over "the field with one element", denoted by $F_{1}$ , and the Hall algebra of $\text…

math.RA2020

Ore Extensions and Infinite Triangularization

Miodrag Iovanov, Jeremy Edison, Alexander Sistko

We give infinite triangularization and strict triangularization results for algebras of operators on infinite dimensional vector spaces. We introduce a class of algebras we call Or…

math.RA2018

On Isoclasses of Maximal Subalgebras Determined by Automorphisms

Alexander H. Sistko

Let $k$ be an algebraically-closed field, and let $B = k Q / I$ be a basic, finite-dimensional associative $k$ -algebra with $n := dim_{k} B < \infty$ . Previous work shows that the colle…

math.RA2018★ 1 cited

Automorphism Groups of Finite-Dimensional Algebras Acting on Subalgebra Varieties

Alexander H. Sistko

Let $k$ be an algebraically-closed field, and $B$ a unital, associative $k$ -algebra with $n := dim_{k} B < \infty$ . For each $1 \leq m \leq n$ , the collection of all $m$ -dimensional su…

math.RA2017

Maximal Subalgebras of Finite-Dimensional Algebras

Miodrag Iovanov, Alexander Sistko

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obt…

math.RA2016

On the Toeplitz-Jacobson algebra and direct finiteness

Miodrag C Iovanov, Alexander Sistko

We study the representation theory of the algebraic Toeplitz algebra $R = K ⟨ x, y ⟩ / ⟨ x y - 1 ⟩$ , give a few new structure and homological theorems, compl…